Tourists from around Asia queue up for cutting-edge $1,000 appliances to boil, steam and store the staple food

The foreign shoppers jamming Tokyo’s electronics shopping district of Akihabara these days probably aren’t looking for TVs and stereos. Instead, many are searching for a different kind of high-tech bounty: Japanese rice cookers.

Decades ago, Japanese companies brought cutting-edge technology to the national obsession with perfectly cooked rice, making appliances—largely for domestic consumption—that offer granular control of boiling, steaming and storage and can sell for anywhere from $400 to more than $1,000. Some models...